Lp-Theory for Vector Potentials and Sobolev's Inequalities for Vector Fields

Chérif Amrouche (1) , Nour El Houda Seloula (2)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 CONCHA - Complex Flow Simulation Codes based on High-order and Adaptive methods

In a three dimensional bounded possibly multiply-connected domain, we prove the existence and uniqueness of vector potentials in Lp theory, associated with a divergence-free function and satisfying some boundary conditions. We also present some results concerning scalar potentials and weak vector potentials. Furthermore, variousSobolev-type inequalities are given.

Domaines: Equations aux dérivées partielles [math.AP]

Chérif Amrouche, Nour El Houda Seloula. Lp-Theory for Vector Potentials and Sobolev's Inequalities for Vector Fields. Discrete and Continuous Dynamical Systems - Series S, 2010, 3 (2), pp.159-183. ⟨10.3934/dcdss.2010.3.159⟩. ⟨hal-00629127⟩